Question

Resistance training is a popular form of conditioning aimed at enhancing sport performance and is widely used among high school, college and professional athletes. A random sample of   270 patients of three age groups (adolescents, young adults and older adults) admitted to the emergency rooms with the injury code “weightlifting” was obtained. These injuries were classified as “accidental” if caused by dropped weight or improper equipment use. Is age and sport injury related?

Age Group	Accidental	Not accidental	Total
Adolescents	30	10	40
Young adults	65	90	155
Older adults	25	50	75
Total	120	150	270

a.       Set the hypothesis testing Ho and H1 for chi square

b.      Use the chi square formula and procedure to solve the problem (as shown in the PPT presentation and textbook pp. 269-70).

c.      Discuss the result. What does the result tell us? Is there a significant relationship between age and injury?

Answer 1

a)

Ho:  age and sport injury are independent

H1: age and sport injury are related

b )

degree of freedom =(row-1)*(column-1)=(3-1)*(2-1)=2

for 2 df and 0.05 level rejection region >5.991

applying chi square test of independence:

Observed	Oi	accidental	not accidental	Total
	Adolescent	30	10	40
	Young adults	65	90	155
	older adults	25	50	75
	Total	120	150	270
Expected	Ei=?row*?column/?total	accidental	not accidental	Total
	Adolescent	17.7778	22.222	40
	Young adults	68.889	86.111	155
	older adults	33.333	41.667	75
	Total	120	150	270
chi square	=(Oi-Ei)2/Ei	accidental	not accidental	Total
	Adolescent	8.403	6.722	15.125
	Young adults	0.220	0.176	0.395
	older adults	2.083	1.667	3.750
	Total	10.706	8.565	19.270

from abvoe as test statistic 19.270 is in rejection region we reject the null hypothesis

c)

as we reject null hypothesis we have sufficient evidence at 0.05 level to conclude that  age and sport injury related